In a steering system of this kind, where the assistance torque is generated by an electric motor, a `boost curve` is needed. The boost curve defines the static relationship between the driver applied input torque and the assistance torque produced by the motor. In a simple system, where a linear relationship exists between input torque and output torque, the boost curve may take the form of a straight line.
In a real application, a simple `straight line` boost curve does not produce satisfactory results. A practical boost curve has several features which provide for an improved driver feel. Firstly, it is desirable to provide for a low-gain region of the curve for small input torques on each side of zero input torque. In the low-gain region, assistance torque is small. This ensures that the steering system is not unnecessarily sensitive to very small adjustments in input torque when travelling in a straight line, for example when maintaining the position of the vehicle in a lane on a highway, but can provide a "progressive" feel when cornering at high vehicle speeds.
Another desirable feature of a practical boost curve is that the gradient of the curve should be high at high levels of input torque. Such high input torques usually occur during parking manoeuvres, and this feature ensures that movement of the steering wheel is eased during such manoeuvres by providing a `light` steering feel. High input torque could also occur at high vehicle speed during an emergency evassive manoeuvre such as a lane change If the gradient of the curve is high, the curve can be said to have a high gain.
A third desirable feature is that there should be a smooth transition between the low-gain region (for low input torques) and the high gain region (for high input torques). Any sudden step changes in gradient of the curve would be apparent to the driver and produce an unpredictable steering feel.
A final feature of a practical boost curve is that there should be a limit on the level of assistance torque which can be applied by the motor. In many systems, this limit is imposed by limitations of the hardware (i.e. maximum torque of the motor). In other systems, the limit may need to be artificially introduced. Where such a limit exists, the boost curve will be flat (i.e. output torque constant) for input torques which would otherwise result in an assistance torque in excess of the limiting value.
Many of these features are well-known from hydraulic power assisted steering systems. Typically, in a hydraulic system the shape of the boost curve is determined by the profile of a rotary valve which permits varying flow rates of hydraulic fluid at different steering input torques. In an electrical power steering system, the boost curve is preferably provided electronically, for example by a software algorithm. This has the advantage that by providing a speed sensor to measure vehicle speed, it becomes possible to alter the size and shape of the boost curve for varying speeds. One such alteration might be an increase in the width of the low-gain region and reduction in the gain of the low gain region at higher speeds to provide an increase in the perceived stability of the vehicle.
In the past, the boost curve has been generated in the form of a piecewise linear approximation of a curve. Such a boost curve comprises a number of portions, each defined by a linear equation. By altering the parameters of the linear equation over each portion, a complex boost curve can be constructed. An example of one such curve is shown in FIG. 1(a) of the drawings.
A disadvantage of the use of a boost curve in which each portion is defined by a linear equation is that it is not smooth as sudden step changes in gradient occur at the transition from one linear portion to another. This is clearly apparent when a plot is made of the derivative of the boost curve, which features many discontinuities as shown in FIG. 1(b). An improvement in the smoothness of the curve can be obtained by increasing the number of linear equations used and thereby reducing the width of each portion, but this considerably increases the complexity of the curve. Furthermore, changes in the shape of the boost curve cannot readily be achieved due to the high number of variables required to generate the entire curve.